Question

Let $f:R\to R$ be a function defined by $f\left(x\right)=-\frac{|x{|}^3+|x|}{1+x^2}$, then the graph of $f\left(x\right)$ lies in the

• A. I and II quadrants
• B. I and III quadrants
• C. II and III quadrants
• D. III and IV quadrants

Answer 1

Answer: (D)

III and IV quadrants

$f\left(x\right)=-\frac{|x{|}^3+|x|}{1+x^2}$
We know, for all R, $|x|\ge 0,x^2\ge 0$
$\Rightarrow \frac{|x{|}^3+|x|}{1+x^2}\ge 0$
Therefore $f\left(x\right)\le 0$, Also domain of f is $R$
Hence f will lie in 3rd and 4th quadrants